Most of our results concern finitary set functors. Recall
that a functor is finitary if it preserves filtered
colimits. Over \(\mathbf {Set} \) , we have the following equivalent
characterizations:
[Adámek and Trnkova [1]}]
Let \(T: \mathbf {Set} \rightarrow \mathbf {Set} \)  be a functor. Then the following are
equivalent:
